WAEC 2016 · Paper 2 · Q2

(a)
If $\dfrac{m}{m - y + 2} = \dfrac{r}{y + r - 1}$ , make $y$ the subject of the equation.
(b)
In a school, $60\%$ of the girls and $70\%$ of the boys own a bicycle. If a boy and a girl are selected at random from the school, find the probability that only one of them owns a bicycle.

Worked solution (try it first)

(a)

Cross-multiply: $m(y + r - 1) = r(m - y + 2)$ .
Expand: $my + mr - m = mr - ry + 2r$ .
The $mr$ terms cancel: $my - m = -ry + 2r$ .
Collect the $y$ terms on the left: $my + ry = m + 2r$ .
Take out $y$ : $y(m + r) = m + 2r$ .
So $y = \frac{m + 2r}{m + r}$ .

(b)

A girl owns a bicycle with probability $0.6$ (so doesn't with $0.4$ ).
A boy with $0.7$ (doesn't with $0.3$ ). "Only one of them" happens in two ways.
The girl owns one and the boy doesn't: $0.6 \times 0.3 = 0.18$ .
The boy owns one and the girl doesn't: $0.7 \times 0.4 = 0.28$ .
Add the two ways: $0.18 + 0.28 = 0.46 = \frac{23}{50}$ .

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